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Abstract

Signal‐to‐interference ratio (SIR) expressions for a doubly spread target are derived for both broadband and narrow‐band transmit signals. For broadband signals, the SIR is dependent upon target and reverberation two‐frequency correlation functions and upon the transmit and processing waveforms. For wide‐sense stationary uncorrelated spreading (WSSUS) communication channels (which implies narrow‐band transmissions), the SIR is dependent upon target and reverberation scattering functions and the cross‐ambiguity function of the transmit and processing waveforms. Volume reverberation and target two‐frequency correlation functions and scattering functions are derived. Volume reverberation is modeled as the spatially uncorrelated scattered field from randomly distributed point scatterers in deterministic plus random translational motion. A single scattering approximation is used and frequency‐dependent directivity functions and attenuation due to absorption are included. A probability density function of random Doppler shift due to the random motion of the scatterers is also derived. Computer plots of the density function are presented as a function of the standard deviation of the random motion. The target is modeled as a linear array of discrete highlights in deterministic translational motion. Example scattering function calculations are presented. The volume reverberation scattering function predicts Doppler spreading as a function of both beam steering angle and random motion of the scatterers. The target scattering function also predicts a spread in Doppler values. Both scattering functions predict time spread and/or contraction as a function of Doppler spread.

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The article of record as published may be found at https://doi.org/10.1121/1.388260

This paper is based on Chaps 3. and 4 of L.J. Ziomek's Ph.D. dissertation "A Scattering Function Approach to Underwater Acoustic Detection and Signal Design, "The Pennsylvania State University (1981).

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